Naphthalene, C-10H8, is a polycyclic aromatic hydrocarbon (PAH) consisting of two fused benzene rings. From previous studies, it is known to form three different commensurate structures in thin epitaxial films on Cu(111), depending on the preparation conditions. One of these structures even exhibits a chiral motif of molecular rotations within the unit cell. In an attempt to elucidate this polymorphism, we performed in situ low-energy electron diffraction (LEED) as a function of temperature and surface coverage, revealing an unexpected and extraordinarily complex structural and thermodynamic behavior. We present experimental evidence for a phase transition from a two-dimensional gas to a highly ordered molecular solid via an intermediate metastable phase with moderate order (extending over a few lattice constants only) which undergoes a reversible orientational shift upon temperature variation. At monolayer coverage and above, we find that two different point-on-line (POL) coincident epitaxial relations constitute the dominant structures. This is remarkable because, so far, POL structures of naphthalene on Cu(111) and other substrates have either not been recognized or not obtained under the respective experimental conditions. Our results are corroborated by the analysis of characteristic moire patterns observed in scanning tunneling microscopy (STM), indicative of a noncommensurate epitaxial registry.